Coarse Granular Media Research Articles

Effects of fluid composition in fluid injection experiments in porous media

Experiments on fluid flow in porous media, using fluids loaded with solids of various grain sizes, have been conducted in a modified Hele-Shaw setup. This setup utilised weakly cemented porous media with specific hydraulic and mechanical properties. Fluid injection in coarse granular media with clean or low-concentration fine particles, results in infiltration only, with pressure close to the material tensile strength, while injection in finer granular material causes damage alongside infiltration, with the fluid pressure still close to the material tensile strength. When larger particle sizes or higher particle concentrations are used in the mixture, the fluid travels further within the porous medium, primarily influenced by the grain size of the granular medium. In the latter case, the Darcy flow equation with an effective permeability term can be employed to determine the pressure differential. For the largest particle sizes included in the fluid, the equation is still applicable, but the effective permeability requires adjustment for particle size within the fluid rather than the granular medium. This is crucial when the injection point is locally clogged. The experiments show that fracturing conditions are controlled by different mechanisms. Dimensional and statistical analysis was used to classify the injection pressures to regimes predicted by fracturing theory or by Darcy law with modified effective permeabilities. The findings show that both the material properties and fluid composition are important designing parameters.

Fibrous coalescence filtration in treating oily wastewater: A review

Many industries discharge oil-in-water emulsion in the waste stream, often above the permissible limit causing serious environmental hazards. Porous media such as membrane and coalescence beds are employed to treat oily wastewater. A coalescence bed filter consists of either fibrous or granular packing and is used for removing larger oil droplets less than 100 μm from secondary emulsions. Fibrous media have higher porosities and specific surface areas than coarse granular media and hence give higher oil removal efficiency. To design an efficient fibrous coalescence bed filter for treating industrial discharge, understanding the mechanism of oil separation is important. This involves the surface wettability of fibers relating to surface chemistry and roughness. Further, fiber diameter, filter bed’s height, porosity, and pore size in relation to the oil droplet size and throughput and influent oil concentration are interactive parameters that affect the efficiency of coalescence. The performance of coalescence filtration is evaluated by analyzing the oil concentrations and D50 droplet sizes in the influent and effluent. In this article, the above-mentioned subjects are comprehensively reviewed from the reported research works, which highlights the complex nature of fibrous coalescence filtration.

A Unified View of Nonlinear Resistance Formulas for Seepage Flow in Coarse Granular Media

There are many studies on the nonlinear relationship between seepage velocity and hydraulic gradient in coarse granular materials, using different approaches and variables to define the resistance formula applicable to that type of granular media. On the basis of an analysis of the existing formulations developed in different studies, we propose an approach for comparing the results obtained by some of the most important studies on state-of-the-art seepage flow in coarse granular media.

Collector efficiency for hydrosol deep-bed filtration of non-Brownian particles at low and finite Reynolds numbers

Aqueous filtration systems with granular media are increasingly implemented as a unit operation for the treatment of urban waters. Many of these aqueous filtration systems are designed with coarse granular media and are therefore subject to finite granular Reynolds numbers (Reg). In contrast to the Reg conditions generated by such designs, current hydrosol filtration models, such as the Yao and RT models, rely on a flow solution that is derived within the Stokes limit at low Reg. In systems that are subject to these finite and higher Reg regimes, the collector efficiency has not been examined. Therefore, in this study, we develop a 3D periodic porosity-compensated face-centered cubic sphere (PCFCC) computational fluid dynamics (CFD) model, with the surface interactions incorporated, to investigate the collector efficiency for Reg ranging from 0.01 to 20. Particle filtration induced by interception and sedimentation is examined for non-Brownian particles ranging from 1 to 100 μm under favorable surface interactions for particle adhesion. The results from the CFD-based PCFCC model agreed well with those of the classical RT and Yao models for Reg < 1. Based on 3150 simulations from the PCFCC model, we developed a new correlation for vertical aqueous filtration based on a modified gravitation number, NG*, for the initial deep-bed filtration efficiency at lower yet finite (0.01 to 20) Reg. The proposed PCFCC model has low computational cost and is extensibile from vertical to horizontal filtration at low and finite Reg.

Two Improvements to Gardner's Method of Measuring the Hydraulic Conductivity of Non‐saturated Media: Accounting for Impedance Effects and Non‐constant Imposed Suction Increment

AbstractGardner's (1956, https://doi.org/10.2136/sssaj1956.03615995002000030006x) transient method of measuring the hydraulic conductivity function of unsaturated media has been largely used, together with the improved graphical method proposed by Kunze and Kirkham (1962, https://doi.org/10.2136/sssaj1962.03615995002600050006x) to account for the impedance effect resulting from using a low hydraulic conductivity ceramic disk in porous plate testing. These methods are nowadays seldom used, since they have been replaced by numerical back analysis and methods for parameter optimization. Based on tests carried out on a specific device allowing to determine the water retention and transport properties of water in a coarse granular media at low suctions (up to 50 kPa), it was found necessary to account (i) for impedance effects and (ii) for the effects of nonconstant suction increments, as is often the case when using the hanging column technique. A new method is proposed to account for impedance effects, based on an analytical solution of the equations governing water transfer. The validity of this method is tested by considering experimental data from three distinct materials: a coarse green roof volcanic substrate, poorly graded sand, and undisturbed silty clay. Compared to the graphical method Kunze and Kirkham's method, it is less operator‐dependent and hence more objective. It is also simpler than numerical back analysis methods, since it does not require any use of numerical code or parameter optimization algorithm, providing a more direct and reliable access to the hydraulic conductivity. An analytical solution is also proposed to solve the problem resulting from the application of a nonconstant suction increment.

An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation

Behaviour of flow resistance with velocity is still undefined for post-laminar flow through coarse granular media. This can cause considerable errors during flow measurements in situations like rock fill dams, water filters, pumping wells, oil and gas exploration, and so on. Keeping the non-deviating nature of Wilkins coefficients with the hydraulic radius of media in mind, the present study further explores their behaviour to independently varying media size and porosity, subjected to parallel post-laminar flow through granular media. Furthermore, an attempt is made to simulate the post-laminar flow conditions with the help of a Computational Fluid Dynamic (CFD) Model in ANSYS FLUENT, since conducting large-scale experiments are often costly and time-consuming. The model output and the experimental results are found to be in good agreement. Percentage deviations between the experimental and numerical results are found to be in the considerable range. Furthermore, the simulation results are statistically validated with the experimental results using the standard ‘Z-test’. The output from the model advocates the importance and applicability of CFD modelling in understanding post-laminar flow through granular media.

Validity of Forchheimer Equation in Radial Flow through Coarse Granular Media

The validity of application of the Forchheimer equation for steady non-Darcy radial flow through coarse granular media and glass spheres has been investigated experimentally. The drawbacks observed while computing the coefficients of this equation have been critically reviewed. An expression is obtained for hydraulic gradient in the case of radial flow. For coarse granular media, a relationship between specific surface and volume diameter has been obtained. In the range of experiments conducted lying in turbulent regime (300 < R < 7,000) a simple form of expression absorbing the effects of variations in size of the medium, number of sizes of the samples used, and porosity of the medium relating resistance to flow and flow pattern in a converging flow configuration is developed. Porosity effect and wall effect are included to make the results of the study more realistic and practically applicable.

On the one-dimensional steady and unsteady porous flow equations

Porous flow in coarse granular media is discussed theoretically with special concern given to the variation of the flow resistance with the porosity. For steady state flow, the Navier-Stokes equation is applied as a basis for the derivations. A turbulent flow equation is suggested. Alternative derivations based on dimensional analysis and a pipe analogy, respectively, are discussed. For non-steady state flow, the derivations are based on a cylinder/sphere analogy leading to a virtual mass coefficient. For the fully turbulent flow regime, existing experimental data values of the quadratic flow resistance coefficients are presented. Moreover, a simple formula for estimation of the turbulent flow coefficient is given. Virtual mass coefficients based on existing data are presented, however, no definite conclusions can be given due to the scarce data available.

Closure to “Virtual Mass of Coarse Granular Media”

Closure to “Virtual Mass of Coarse Granular Media”

Air-Water Flow in Coarse Granular Media

Air may be entrained in the flow in porous shore structure under wave action. Three conceptual models for two-phase flow in ducts have been adapted to describe flow in coarse granular media. These are the homogeneous, bubbly drift-flux, and slug drift-flux models. An experimental study was undertaken to check the three models against air-water flow in three coarse granular porous media. The best model was chosen based on its agreement with the experimental head drop results. On this basis the slug flow drift-flux model is recommended to calculate the effect of entrained air on the hydraulic conductivity for co-current and counter current flows.

WAVE ENERGY DISSIPATION IK ROCKFILL

Very little literature exists on the subject of unsteady non-Darcy flow in coarse granular media. However, unsteady non-Darcy flow is encountered in a few important hydraulic problems, for example, (a) Wave absorption and transmission in rubble-mound break-waters; (b) Water level fluctuations in the rockfill and filter zones of a dam subjected to wave action; (c) Transmission of floods or tides through rockfill dams and causeways, A mathematical model, to simulate the internal Darcy and/or non-Darcy flow in an embankment subjected to wave action, would permit an improved analysis of: the stability of the embankment; the stability of the armour layer; and the absorption and dissipation of wave energy by the rockfill. Since the internal flow in the embankment and the external wave action are interdependent, a complete model requires the simulation of both of these flows. Such a model would permit the computation of wave run-up and reflection. The present report is limited to the simulation of the unsteady internal flow. Heitner and Housner (4), using a finite element method, have developed an external wave action simulation for Tsunamis. The author is presently attempting to couple the internal and external models.

Nonlinear Flow in Porous Media by Finite Elements

Two commonly suggested forms of the equation linking head loss and velocity for flow of water through coarse granular media are the Forchheimer and exponential relations. Combined with the continuity expression, these relations give the differential equations applicable, within the limits of validity of the parent relations, to actual regions of flow. The resultant nonlinear partial differential equations are amenable to solution by the numerical technique known as the method of finite elements. This technique has advantages when dealing with complex boundary shapes. Solutions have been obtained for some examples of unconfined flow with boundary conditions similar to those likely to be encountered in practical applications. Experimental work in an open flume has shown that agreement between observed and calculated values of discharge and piezometric head can be obtained when the coefficients in the head loss equations are accurately known.

An experimental study of the flow of water through coarse granular media

An experimental study of the flow of water through coarse granular media